Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userImproving Network Robustness through Edge Augmentation While Preserving Strong Structural Controllability
104
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper, we consider a network of agents with Laplacian dynamics, and study the problem of improving network robustness by adding a maximum number of edges within the network while preserving a lower bound on its strong structural controllability (SSC) at the same time. Edge augmentation increases networks robustness to noise and structural changes, however, it could also deteriorate network controllability. Thus, by exploiting relationship between network controllability and distances between nodes in graphs, we formulate an edge augmentation problem with a constraint to preserve distances between certain node pairs, which in turn guarantees that a lower bound on SSC is maintained even after adding edges. In this direction, first we choose a node pair and maximally add edges while maintaining the distance between selected nodes. We show that an optimal solution belongs to a certain class of graphs called clique chains. Then, we present an algorithm to add edges while preserving distances between a certain collection of nodes. Further, we present a randomized algorithm that guarantees a desired approximation ratio with high probability to solve the edge augmentation problem. Finally, we evaluate our results on various networks.
rate research
Read More
In linear control theory, a structured system is a system whose entries of its system matrices are either fixed zero or indeterminate. This system is structurally controllable, if there exists a realization of it that is controllable, and is strongly structurally controllable (SSC), if for any nonzero values of the indeterminate entries, the corresponding system is controllable. This paper introduces a new controllability notion, termed partial strong structural controllability (PSSC), which naturally extends SSC and bridges the gap between structural controllability and SSC. Dividing the indeterminate entries into two categories, generic entries and unspecified entries, a system is PSSC, if for almost all values of the generic entries in the parameter space except for a set of measure zero, and any nonzero (complex) values of the unspecified entries, the corresponding system is controllable. We highlight that this notion generalizes the generic property embedded in the conventional structural controllability for single-input systems. We then give algebraic and (bipartite) graph-theoretic necessary and sufficient conditions for single-input systems to be PSSC. Conditions for multi-input systems are subsequently given for a particular case. We also extend our results to the case where the unspecified entries can take either nonzero values or zero/nonzero values. Finally, we show the established results can induce a new graph-theoretic criterion for SSC in maximum matchings over the system bipartite graph representations.
Robustness against adversarial attack in neural networks is an important research topic in the machine learning community. We observe one major source of vulnerability of neural nets is from overparameterized fully-connected layers. In this paper, we propose a new neighborhood preserving layer which can replace these fully connected layers to improve the network robustness. We demonstrate a novel neural network architecture which can incorporate such layers and also can be trained efficiently. We theoretically prove that our models are more robust against distortion because they effectively control the magnitude of gradients. Finally, we empirically show that our designed network architecture is more robust against state-of-art gradient descent based attacks, such as a PGD attack on the benchmark datasets MNIST and CIFAR10.
This paper develops tools to quantify the importance of agent interactions and its impact on global performance metrics for networks modeled as linear time-invariant systems. We consider Gramian-based performance metrics and propose a novel notion of edge centrality that encodes the first-order variation in the metric with respect to the modification of the corresponding edge weight, including for those edges not present in the network. The proposed edge centrality matrix (ECM) is additive over the set of inputs, i.e., it captures the specific contribution to each edges centrality of the presence of any given actuator. We provide a full characterization of the ECM structure for the class of directed stem-bud networks, showing that non-zero entries are only possible at specific sub/super-diagonals determined by the network size and the length of its bud. We also provide bounds on the value of the trace, trace inverse, and log-det of the Gramian before and after single-edge modifications, and on the edge-modification weight to ensure the modified network retains stability. Simulations show the utility of the proposed edge centrality notion and validate our results.
In this paper, we study the maximum edge augmentation problem in directed Laplacian networks to improve their robustness while preserving lower bounds on their strong structural controllability (SSC). Since adding edges could adversely impact network controllability, the main objective is to maximally densify a given network by selectively adding missing edges while ensuring that SSC of the network does not deteriorate beyond certain levels specified by the SSC bounds. We consider two widely used bounds: first is based on the notion of zero forcing (ZF), and the second relies on the distances between nodes in a graph. We provide an edge augmentation algorithm that adds the maximum number of edges in a graph while preserving the ZF-based SSC bound, and also derive a closed-form expression for the exact number of edges added to the graph. Then, we examine the edge augmentation problem while preserving the distance-based bound and present a randomized algorithm that guarantees an approximate solution with high probability. Finally, we numerically evaluate and compare these edge augmentation solutions.
We study the strong structural controllability (SSC) of diffusively coupled networks, where the external control inputs are injected to only some nodes, namely the leaders. For such systems, one measure of controllability is the dimension of strong structurally controllable subspace, which is equal to the smallest possible rank of controllability matrix under admissible (positive) coupling weights. In this paper, we compare two tight lower bounds on the dimension of strong structurally controllable subspace: one based on the distances of followers to leaders, and the other based on the graph coloring process known as zero forcing. We show that the distance-based lower bound is usually better than the zero-forcing-based bound when the leaders do not constitute a zero-forcing set. On the other hand, we also show that any set of leaders that can be shown to achieve complete SSC via the distance-based bound is necessarily a zero-forcing set. These results indicate that while the zero-forcing based approach may be preferable when the focus is only on verifying complete SSC, the distance-based approach is usually more informative when partial SSC is also of interest. Furthermore, we also present a novel bound based on the combination of these two approaches, which is always at least as good as, and in some cases strictly greater than, the maximum of the two bounds. We support our analysis with numerical results for various graphs and leader sets.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
